The technical field of this invention is brushless DC motors, and particularly such motors optimized for use in a vibration sensitive environment such as an electric power steering system for a vehicle.
In a conventional three-phase, trapezoidal back EMF, brushless DC motor, the three phase windings are distributed on the stator surface over 6 phase belts of 60 electrical degrees each. The conductors for each phase belt are placed in a single or multiple slots over this 60 degrees. FIG. 2 shows a prior art example of such a motor 1 having a four pole PM rotor 2 and a stator 3 with windings for phases A, B and C placed in 12 stator slots 4 of 60 electrical degrees (30 mechanical degrees) each. FIG. 3 shows a motor 5 which is a prior art variation of motor 1 in FIG. 2. Motor 5 has a similar four pole rotor 6 and a stator 7 having twenty-four stator slots 8, with each slot comprising only 30 electrical degrees (15 mechanical degrees) but with windings in pairs of adjacent slots connected in the same phase, so that the windings for phases A, B and C are still each distributed over phase belts of 60 electrical degrees.
In order to reduce cogging torque in such motors, either the stator slots or the rotor magnets are skewed to produce a skew of one slot pitch therebetween axially across the stator. Under such conditions, assuming an ideal square wave flux distribution in the air gap and a nearly closed slot structure, the line-to-line back EMF waveform generated by the rotating rotor across each pair of phase terminals has a trapezoidal shape with a flat top indicating a constant value over a range of 60 electrical degrees. In an ideal case wherein each phase is excited by a constant current over 120 degrees, a ripple free torque would be produced. However, in reality, the flux distribution in the air gap is not a square wave; and this results in a line-to-line back EMF wave form which droops at each end of the 60 degree "flat" area. In FIG. 9, the actual back EMF curves V.sub.cb, V.sub.ab and V.sub.ac of the motor of FIG. 3 are shown for a portion of a rotor rotation. The portions of the back EMF curves which produce motor torque, because current is provided through the indicated terminals, are shown as solid lines; and the remainder of the curves, which produce no torque, are shown as dashed lines. It can be seen that, from 60 to 120 electrical degrees, only curve V.sub.ab is active in generating torque. The solid line portion of curve V.sub.ab illustrates that the back EMF in this range is not constant: it achieves a maximum at 90 degrees and droops by about 12 percent of that maximum torque at 60 and 120 degrees. This occurs for each curve over the range of 60 electrical degrees of motor rotation in which it produces torque; and the result is a torque ripple which can be undesirable in some motor applications. In particular, such a motor used as a direct actuator in an electric power steering system for a motor vehicle will be mounted on and/or coupled to the vehicle steering column; and vibrations produced by the torque ripple may be conducted directly to the steering wheel, where they may be both apparent and annoying to the vehicle operator.